﻿<p>An <em>IfcEllipse</em> is a curve consisting of a set of points whose distances to two fixed points add to the same
constant.</p>
<p>The inherited <em>SELF\IfcConic.Position.Location</em> is the center of the <em>IfcEllipse</em>, and the inherited
S<em>ELF\IfcConic.Position.Position.P[1]</em> is the direction of the <em>SemiAxis1</em>.</p>
<table summary="example" cellpadding="2" cellspacing="2">
<tr>
<td><img src="../../../figures/ifcellipse-layout1.gif" alt="ellipse" width="400" height="300" border="0"></td>
<td style="vertical-align:bottom; text-align:left;">
<p><span style="font-size:smaller">Definition of the <em>IfcEllipse</em> within the a three-dimensional position
coordinate system is shown in Figure 2.</span></p>
<p><span style=" font-size:smaller;">It is placed within the object coordinate system of an element of which it is a
representation.</span></p>
</td>
</tr>
<tr>
<td>
<p class="figure">Figure 2 &mdash; Ellipse placement and parameterization</p>
</td>
<td>&nbsp;</td>
</tr>
</table>
<blockquote class="note">NOTE&nbsp; An elliptical arc segment is defined by using the <em>IfcTrimmedCurve</em> with
<em>BasisCurve</em></blockquote>
<blockquote class="extDef">
<p style=" font-size:inherit;">NOTE Definition according to ISO/CD 10303-42:1992<br>
An ellipse is a conic section defined by the lengths of the semi-major and semi-minor diameters and the position
(center or mid point of the line joining the foci) and orientation of the curve. Interpretation of the data shall be as
follows:</p>
<blockquote><code style="font-size:small;">C = position.location<br>
x = position.p[1]<br>
y = position.p[2]<br>
z = position.p[3]<br>
R1 = semi axis 1<br>
R2 = semi axis 2</code></blockquote>
<p style=" font-size:inherit;">and the ellipse is parameterized as:</p>
<blockquote><img alt="formula" src="../../../figures/ifcellipse-math1.gif" width="220" height="22"></blockquote>
<p style=" font-size:inherit;">The parameterization range is 0 &le; <i>u</i> &lt;&le; 2&pi; (0 &le; <i>u</i> &le; 360
degree). In the placement coordinate system defined above, the ellipse is the equation <i>C</i> = 0, where</p>
<blockquote>
<p style=" font-size:inherit;"><img alt="formula" src="../../../figures/ifcellipse-math2.gif" width="193" height="24"></p>
</blockquote>
<p style=" font-size:inherit;">The positive sense of the ellipse at any point is in the tangent direction, T, to the
curve at the point, where</p>
<blockquote>
<p style=" font-size:inherit;"><img alt="formula" src="../../../figures/ifcellipse-math3.gif" width="102" height="25"></p>
</blockquote>
</blockquote>
<blockquote class="note">NOTE&nbsp; Entity adapted from <strong>ellipse</strong> defined in ISO
10303-42</blockquote>
<blockquote class="history">HISTORY&nbsp; New entity in IFC1.0</blockquote>